PreprintCC BY 4.0arXiv
On partitions with bounded multiplicity restrictions on even parts and with the largest part being odd
Abstract
Andrews and El Bachraoui (\textit{RACSAM} \textbf{119}, \textit{Article Number 4 (2025)}) established identities relating $4$-regular partitions to partitions with distinct even parts whose largest part is odd. As an extension to their work, in this paper we define partitions of a positive integer n with bounded multiplicity restriction on even parts and whose largest part is odd. We prove some identities relating our partition functions and 2r-regular partition function, and show that identities due to Andrews and El Bachraoui follow as particular cases.
Related
- Maximum length and size of simultaneous core partitions with distinct parts
- A uniform proof approach for congruences modulo 3 for partitions with k-colored odd parts
- Bounds for Unions of Several Parts in Balanced Graph Partitions
- Largest-dihedral-angle bisection algorithm does not preserve mesh regularity for tetrahedral partitions
- Congruences modulo powers of $7$ for partitions with colored odd parts
BibTeX
@misc{bardhan2026partitions,
title = {{On partitions with bounded multiplicity restrictions on even parts and with the largest part being odd}},
author = {Gaurab Bardhan and Nipen Saikia},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05160},
eprint = {2611.05160},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05160},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On partitions with bounded multiplicity restrictions on even parts and with the largest part being odd
AU - Gaurab Bardhan
AU - Nipen Saikia
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05160
UR - https://arxiv.org/abs/2611.05160
AB - Andrews and El Bachraoui (\textit{RACSAM} \textbf{119}, \textit{Article Number 4 (2025)}) established identities relating $4$-regular partitions to partitions with distinct even parts whose largest part is odd. As an extension to their work, in this paper we define partitions of a positive integer n with bounded multiplicity restriction on even parts and whose largest part is odd. We prove some identities relating our partition functions and 2r-regular partition function, and show that identities due to Andrews and El Bachraoui follow as particular cases.
ER -